Salvete omnes

The idea that the Argei - the straw puppets tossed into the Tiber at a ceremony on 17 March - were substitutions for earlier human sacrifices was an interpretation first presented in the Late Republic. The Romans did not have a very good understanding of some of their customs, offering explanations that were often wild inventions rather than based in any traditional explanations. They also tended to project their interpretations into a far distant past, when they did not have a very good conception of time. Basically anything older than their grandfathers was ancient and projected back in time to a very early date. Everything about the religio Romana that authors of the Late Republic mention may in fact be no earlier than the fourth century. That is, what the Romans of the Late Republic attributed to Romulus and to Numa Pompilius may in fact have only begun when the religious institutions of the City were reconstituted follwoing the Gallic sack. It was at that time that oral traditions of the pontifices, and possibly of the augures as well, were first written down. This sacred law, called the Lex Postumna in some sources, was attributed to Numa Pompilius, but can only be considered a body of religious customs as existed in the fourth century.

So, to toss around some ideas... The saculla where the Argei were stored were 24 (or so) shrines within six districts inside the so-called Servian Wall. That wall was not built in the time of King Servius. The stone used in the wall comes from Veii, and in such quantity, that the Servian Wall had to have been built after Rome took Veii, thus dating to the fourth century. It was likely built after and in reaction to the Gallic sack of 360 BCE. These sacella may be comparable to the shrines dedicated to the Lares Compitales that were set up when Augustus reorganized the City and replaced the former vici. That is, they were shrines dedicated to the Manes of particular city districts.

Argei, the plural of Argeus, was understood in the Late Republic to refer to the Greeks (Argives). Thus a story was told that the Argei represented Greek followers of Hercules who was said to have visited the City before the arrival of Romulus and Remus. It is possible that the term did originally refer to Greeks, since it was in the fourth century that Italic tribes and the Latins were attributing their origins to Greek heroes drawn from Homer. The Sabines, as one example, placed their origin among Spartans, and another example is where the Marsi claimed descent from a son of Odysseus by Circe. About the middle of the fourth century the cultus of Aeneas began at Lavinium, which the Romans adopted by the end of the century, reworking a tomb (from the sixth century IIRC) into the heroon of Aeneas around 304 BCE. Another possibility is that the term Argei meant something completely different in the fourth century from what the Romans of the first century thought it meant. It could have meant "the shining ones" as a reference to hallowed ancestors. It could have referred to those Romans of whom Livy mentions, who did not withdraw to the Capitolium during the Gallic sack, but decided to remain in their homes instead, dying as they defended their family shrines. The sacella Argeorum may then have been set up to honor the defenders of the city districts, and later called upon as Lares to help defend and protect the various districts as existed when the City was rebuilt following the Gallic sack.

Why toss the puppets into the Tiber River? As the City was being cleared following that little mishap, the Romans likely did toss a lot of debris into the river. Tossing the bodies of victims into the river would not have been very Roman, but maybe due to the expediancy necessary after such a disaster... Well, they would have had to atone for needing to do such a thing. I can see where on the anniversary of the event of clearing the City of the dead that the Romans may have reenacted that day, mourning the dead as the flaminica Dialis did in the later rite.

I agree with Dumezil that the Argei were not likely substitutes for human sacrifices. And they cannot have originally represented Greek followers of Hercules, as that myth was invented much later. There is no way of knowing what they represented or what was the purpose of the ceremony. If the ritual did extend back only to the fourth century and not earlier, then the above is a possible explanation, but a lot of speculation on my part. Both Late Republican explanations are doubtful, which is about all that can be said about the Argei.